I need to compare two linear regression models that include the regressors in levels and in squares:
$Y=a_1x^2+b_1x+c_1$ and $Y=a_2x^2+b_2x+c_2 $
Specifically, I need to test whether these regression models are significantly different (i.e., whether $a_1=a_2,b_1=b_2,c_1=c_2$).
In the forum, I read that one should build respective interactions.
Yet, I do not exactly understand what is meant by including “interactions.”
What would that model look like? What should be compared with what, and what test statistic is best?
(I do not know Stata, unfortunately.)
Both models are based on /using the exact same population.